Bayesian estimation framework for source separation with mixture densities

Abstract

One of the main signal processing problems in acoustics applications is the sources separation. This problem is inherently an ill-posed problem. The Bayesian inference framework is a coherent way to solve such problems by modeling sources and canals and by combining prior information coming from these probabilistic modeling and information included in the data. In this contribution, after a brief presentation of general source separation problems and the Bayesian inference framework, we present new algorithms to source separation for the case of noisy instantaneous linear mixture, within the Bayesian estimation framework. The prior source distribution is modeled by a mixture of Gaussians and the mixing matrix elements distributions by a Gaussian. We model the mixture of Gaussians hierarchically by means of hidden variables representing the labels of the mixture. Then, we consider the joint a posteriori distribution of sources, mixing matrix elements, labels of the mixture, and other parameters of the mixture with appropriate prior probability laws to eliminate degeneracy of the likelihood function of variance parameters and we propose iterative algorithms to estimate jointly sources, mixing matrix, and hyperparameters: Joint MAP (maximum a posteriori) algorithms.